A273784 Frequency of the largest spectral component of the Moebius function of the first n numbers, for n>0. In case of a tie, use the smallest frequency.

1, 2, 2, 2, 3, 2, 4, 4, 5, 3, 6, 7, 7, 8, 8, 9, 9, 5, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 7, 18, 18, 19, 7, 20, 7, 21, 8, 8, 8, 8, 8, 24, 9, 25, 9, 26, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 32, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14

Offset

1,2

Comments

The Discrete Fourier transform is applied to the list of Moebius function of first n numbers, then it is selected the position of the largest absolute value of the components of the transformed list. If there are several identical maxima then it is taken the lowest position of them.

A curious pattern (see link) shows that frequencies of most maximum spectral components are aligned along few convergent directions.

Links

Table of n, a(n) for n=1..77.

Andres Cicuttin, Scatter plot of first 20000 elements

Example

For the first 60 numbers starting from 1, the absolute values of the discrete Fourier transform of the Moebius function of these numbers have a maximum at position 11, then a(60) = 11.

Mathematica

Table[Position[b=Abs@Fourier@Table[MoebiusMu[j], {j, 1, n}], Max[b]][[1, 1]], {n, 1, 120}]

Crossrefs

Sequence in context: A157231 A332888 A258596 * A318058 A345901 A305434

Adjacent sequences: A273781 A273782 A273783 * A273785 A273786 A273787

Keyword

nonn

Author

Andres Cicuttin, May 30 2016

Status

approved